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arXiv · 1704.04893

Fine Selmer Groups and Isogeny Invariance

R. Sujatha·M. Witte
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Abstract

We investigate fine Selmer groups for elliptic curves and for Galois representations over a number field. More specifically, we discuss Conjecture A, which states that the fine Selmer group of an elliptic curve over the cyclotomic extension is a finitely generated $\mathbb{Z}_p$-module. The relationship between this conjecture and Iwasawa's classical $\mu=0$ conjecture is clarified. We also present some partial results towards the question whether Conjecture A is invariant under isogenies.

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R. Sujatha, M. Witte. 2017-04-17. Fine Selmer Groups and Isogeny Invariance. https://arxiv.org/abs/1704.04893

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